Consider statements $p$ : $S_1$ is closed; $q$ : $S_2$ is closed; $r$ : $S_3$ is closed. The simplified equivalent circuit diagram and its logical statement for the switching circuit is respectively ______.
Show Hint
Always translate the circuit to a Boolean expression first! Use Absorption laws ($p \lor (p \land q) \equiv p$) and Complement laws ($p \lor \sim p \equiv \text{True}$) to rapidly reduce massive parallel/series blocks.
Step 1: Understanding the Concept:
Switching circuits can be represented using symbolic logic. Switches in series correspond to the conjunction ($\land$) and switches in parallel correspond to the disjunction ($\lor$). Step 2: Formula Application:
Use the laws of logic (Distributive, Absorption, De Morgan's, etc.) to simplify the symbolic expression. Step 3: Explanation:
Typically, in these problems, you translate the physical circuit into a statement like $(p \land q) \lor (p \land r)$. By Distributive law, this simplifies to $p \land (q \lor r)$. The equivalent circuit would then be switch $S_1$ in series with a parallel combination of $S_2$ and $S_3$. Step 4: Final Answer:
The simplified circuit matches the reduced logical expression.
